Melt the 1/2 C of butter in a small pan over medium-low heat, stirring occasionally. Butter will crackle and foam a but as it browns. Once butter is light brown and smells nutty, take off heat and transfer to small bowl. Be careful, it goes from brown to black fast.

In a large bowl, whisk together flour, sugar, baking powder, baking soda, salt and cinnamon.

In a small bowl combine egg, buttermilk and vanilla, plus 2 T of the browned butter. Reserve the left over brown butter for the cinnamon sugar coating.

Add wet ingredients into the dry ingredients and mix until combined. Do not over mix.

Place batter into a large ziploc bag and cut about 1/2 " piece off one corner to create a disposable pastry bag. Fill each well in the donut pan approximately 3/4 full.

Bake for 9-12 minutes, checking with a toothpick at 9 to prevent being dry. Remove pan from oven and let sit a couple minutes, then invert pan onto wire rack to cool completely. Once cooled, trim with a knife or scissors any edges to create a round donut. (Don't worry if it looks ugly, the cinnamon sugar topping covers all flaws. And yes, all my donuts have a very flat bottom.)

Combine sugar, brown sugar and cinnamon in a bowl breaking up any lumps.

Using left over brown butter (melt in microwave for 5-10 seconds if it has become too solid) and working quickly one at a time, lightly brush donut with brown butter, and roll around in sugar mixture until will coated. I had best results spooning it all around.

If not eating immediately, cover with plastic wrap or freeze.

*Recipe adapted from sharedappetite.com.
*I've made these several times and I still think the batter is too runny. The original recipe had only 1 C flour and I added a little more. I think next time I will try omitting the extra 2 T buttermilk and see if that helps.
*Made them for Easter Brunch and the 2nd Dessert of the Month Club